Adapting Portfolio Return Equations for Long–Short Models
Summary
The document explores how to adapt a deep reinforcement learning portfolio model, originally formulated for long-only positions, to allow positive and negative weights. The proposed representation makes positive weights long exposures and negative weights short exposures, with the sum of absolute weights constrained to one. The question is how to modify return and portfolio value equations that use asset price-return factors, since applying those factors directly to negative weights may not represent short-position gains and losses correctly.
The author first considers inverting the return factor for short positions, then experiments with an additive return adjustment based on the signed weight. That change appears to work in some equations but fails in another, and the author remains uncertain whether short-position values are computed correctly. No validated formulation, proof, or performance evidence is provided. The note highlights that a long-only portfolio accounting model cannot be extended merely by changing the output weights; short-sale mechanics and consistent portfolio accounting must also be specified.
Key ideas
- The source model assumes nonnegative portfolio weights and long-only exposures.
- Negative weights require return accounting that correctly reflects short-position profits and losses.
- Inverting returns for short positions and adjusting them linearly are proposed but not validated.
- A candidate adjustment fails in one equation, leaving the reformulation unresolved.
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Full text
# transforming a model to long short instead of long-only # transforming a model to long short instead of long-only I am currently trying to adapt a model to a long short portfolio strategy. The model is stated here: A Deep Reinforcement Learning Framework for the Financial Portfolio Management Problem by Jiang, Xu, and Liang https://arxiv.org/abs/1706.10059 In Eq. (1-10), the portfolio process is formulated. The portfolio weight vector w can have only positive values in this long-only setting. Instead, I now adapted the network to output a weight vector of positive and negative values whose absolute values sum up to one, where positive (negative) values represent going long (short). When looking at the equations, one quickly sees that the portfolio equations do not work correctly anymore if the weight vector can have negative values, mostly because of the definition of yt, which is the price return expressed as a factor from time t-1 to t. For instance, yt = vt/v[t-1] where v are the prices of the individual assets. As a first fix, I tried to take 1/yt instead of yt whenever the corresponding weight is negative. Then, in the following equations, I can simply use the absolute of the vector w, and the equations should come out right then. However, in this way, i believe, the network does not really learn to set the weights correctly. Instead, now, i am trying to reformulate the equations correctly for a weight vector that can take negative values, as well. My first try was to replace yt*wt by 1 + (yt-1) * wt in all the equations. This seems to work (although I am not sure whether the values of the short positions are then correctly computed), but for Eq.(7), it fails. So there must be a different, more elegant approach to adapt the model to long short without having to change much in the loss functions, portfolio value computation, etc. Any ideas? I appreciate it! Best, JC
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